This invention relates generally to deployable structures, which may serve for example as antennae, as in space; and more particularly it concerns a rapidly deployable hyperboloidal antenna structure, expansible from collapsed condition (as during launching from earth) to expanded condition, for service as an antenna or reflector, or for similar uses, such as a hyperboloidal structural framework for a space vehicle, artificial satellite or a structure for a machine housing or human habitat on a moon, asteroid or planet.
Throughout history, architects and engineers have sought to design support and bracing systems to withstand stresses within members caused by external forces. These stresses are: tension, compression, shear and torsion, usually acting in combination, giving flexure or bending. These stresses are accentuated in large structures where horizontal stresses become more important than vertical stresses.
One unique geometric shape which can be used as a structure acting to eliminate horizontal forces is that conforming to an hyperboloid of revolution of one sheet, and characterized in that horizontal and vertical forces are transformed into axial forces acting up or down the ruled line truss members in compression or tension, i.e. along directrices or ruled lines of the structure.
The hyperboloid of revolution of one sheet is further characterized by:
(1) the only surface which is both a warped surface and a surface of revolution, PA1 (2) a ruled surface generated by revolving a straight line about an axis that is not in the same plane, PA1 (3) may also be generated by revolving an hyperbola about an axis in the plane of the curve and which is the perpendicular bisector of a line joining the foci, PA1 (4) a peculiar property of the hyperboloid of revolution of one sheet and of the hyperbolic paraboloid is that: through any point on the surface there pass two distinct straight lines which lie entirely in the surface. These lines are called rulings and surfaces which contain rulings are called ruled surfaces. (Note: the hyperbolic paraboloid is not a surface of revolution). PA1 (a) all forces are eliminated except axial forces in the structures, which is a new principle, PA1 (b) the ruled line truss members serve two simultaneous purposes: namely, vertical support and also bracing. PA1 (a) a first framework including multiple frame members extending along the ruled lines or directrices of an hyperboloid of revolution, (a directrix is a ruled line which when revolved about a central axis will generate the entire surface of revolution), PA1 (b) the members having pivotal interconnections at intersections of said directrices, or ruled lines, PA1 (c) whereby the framework is deployable between collapsed and expanded conditions and can be collapsed or expanded repeatedly if desired. PA1 (a) provision of large size and at the same time very light weight (up to 90% less) hyperboloidal antenna to be contained in a small diameter tube or container for trans-orbital insertion, PA1 (b) the antenna is rapidly self-deployable and can be folded back up and stored in the small container for use at any time, PA1 (c) the hyperboloidal antenna is extraordinarily strong and stiff, as in use as a structural system on earth, under gravity and horizontal loads, while being very light, PA1 (d) when opened or closed the device can withstand high G forces, PA1 (e) use of all compression members in prestressed condition to resist tension and compression from any direction while resolving all forces into axial loads, PA1 (f) use of the antenna structure as a habitat and/or equipment bay, PA1 (g) antenna sub-assemblies such as: wiring, power modules, emitters, receptors, computers, attitude-control rockets, fuel tank and all other components can be permanently mounted in structure folded configuration and functionally connected so they are always ready for use, PA1 (h) because of its high geometric and structural redundancy, the structure will withstand extensive damage and can still remain operational, PA1 (i) use of electronic means to shape the electromagnetic wave to match the hyperboloidal structural geometry providing structure that is the antenna, operating with extremely high efficiency.
If a structure is constructed in the shape of an hyperboloid of revolution of one sheet and if all support is by members lying along the ruled lines, as in this invention, then it follows that:
The forces which are eliminated are shear and torsion, leaving only tension and compression. Then if the ruled line members are designed so as to be considered as compression members, the structure must fail first in compression before it can go into tension (under the force of gravity or while undergoing acceleration or deceleration). Therefore, in effect, tension is also eliminated, leaving only the force of compression. This geometry works with natural forces instead of against them. The resulting structure is mathematically determinate and requires no stressing nor destruction testing of models to prove its structural integrity. In space, while in orbit under so-called "free fall", the structure would be subject to axial forces only, i.e., tension and compression acting along the same lines equal and opposite.
Extending the discussion to satellites, and in recognition of the above, there is need for a unitary antenna, reflector or other structure which is easily deployable in space and can utilize the unusually advantageous structural principles of an hyperboloid of revolution.